Proof Step: c_0_313

name: c_0_313 syntax: thf role: plain inference: evalgc

Proof State Overview

proof_step c_0_8 ⊕ divide_divide_real X11 divide_divide_real X15 X40 = divide_divide_real times_times_real X11 X40 X15 c_0_297 ⊕ times_times_real semiri2110766477t_real X2 divide_divide_real X1 semiri2110766477t_real times_times_nat X2 X2 = divide_divide_real X1 semiri2110766477t_real X2 c_0_8->c_0_297 c_0_9 ⊕ times_times_real X11 divide_divide_real X15 X40 = divide_divide_real times_times_real X11 X15 X40 c_0_9->c_0_297 c_0_19 ⊕ divide_divide_real times_times_real X690 X11 times_times_real X690 X690 = divide_divide_real X11 X690 c_0_19->c_0_297 c_0_38 ⊕ semiri2110766477t_real times_times_nat X14 X23 = times_times_real semiri2110766477t_real X14 semiri2110766477t_real X23 c_0_38->c_0_297 c_0_48 c_0_48 c_0_298 ⊕ ord_less_eq_real zero_zero_real X1 ⊕ ord_less_eq_real X5 zero_zero_real ⊖ ord_less_eq_real zero_zero_real times_times_real X5 X1 c_0_48->c_0_298 c_0_313 ⊕ ord_less_eq_real semiri2110766477t_real X2 zero_zero_real ⊕ ord_less_eq_real zero_zero_real divide_divide_real X1 semiri2110766477t_real times_times_nat X2 X2 ⊖ ord_less_eq_real zero_zero_real divide_divide_real X1 semiri2110766477t_real X2 c_0_298->c_0_313 c_0_297->c_0_313 c_0_323 ⊕ $false c_0_313->c_0_323

Input Dependencies

c_0_8 c_0_9 c_0_19 c_0_38 c_0_48

Assumptions

c_0_298 c_0_297

Conclusion

c_0_313

Dependents

c_0_323

Formula

! [X1: real,X2: nat] :
  ( ( ord_less_eq_real @ ( semiri2110766477t_real @ X2 ) @ zero_zero_real )
  | ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X1 @ ( semiri2110766477t_real @ ( times_times_nat @ X2 @ X2 ) ) ) )
  | ~ ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X1 @ ( semiri2110766477t_real @ X2 ) ) ) )

Source

inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_298,c_0_297])])